Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations

Research output: Contribution to journalJournal article – Annual report year: 2018Researchpeer-review

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Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations. / Lee, Jonghyun; Rolle, Massimo; Kitanidis, Peter K.

In: Journal of Contaminant Hydrology, Vol. 212, 2018, p. 41-54.

Research output: Contribution to journalJournal article – Annual report year: 2018Researchpeer-review

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@article{55af40fa0f5a42b1aeeec5aa940a71ea,
title = "Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations",
abstract = "Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large P{\~A}{\circledC}clet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers.",
keywords = "Environmental Chemistry, Water Science and Technology, Heterogeneity and scale, Longitudinal dispersion, Numerical models, Solute transport, Aquifers, Boltzmann equation, Equations of state, Groundwater, Groundwater resources, Hydrogeology, Mass transfer, Parameterization, Perturbation techniques, Porous materials, Relaxation time, Advection-dispersion equation, Computationally efficient, Hydrodynamic dispersions, Longitudinal dispersion coefficient, Longitudinal dispersions, Longitudinal dispersivity, Mass transfer limitation, Dispersions",
author = "Jonghyun Lee and Massimo Rolle and Kitanidis, {Peter K.}",
year = "2018",
doi = "10.1016/j.jconhyd.2017.09.004",
language = "English",
volume = "212",
pages = "41--54",
journal = "Journal of Contaminant Hydrology",
issn = "0169-7722",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations

AU - Lee, Jonghyun

AU - Rolle, Massimo

AU - Kitanidis, Peter K.

PY - 2018

Y1 - 2018

N2 - Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large Péclet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers.

AB - Most recent research on hydrodynamic dispersion in porous media has focused on whole-domain dispersion while other research is largely on laboratory-scale dispersion. This work focuses on the contribution of a single block in a numerical model to dispersion. Variability of fluid velocity and concentration within a block is not resolved and the combined spreading effect is approximated using resolved quantities and macroscopic parameters. This applies whether the formation is modeled as homogeneous or discretized into homogeneous blocks but the emphasis here being on the latter. The process of dispersion is typically described through the Fickian model, i.e., the dispersive flux is proportional to the gradient of the resolved concentration, commonly with the Scheidegger parameterization, which is a particular way to compute the dispersion coefficients utilizing dispersivity coefficients. Although such parameterization is by far the most commonly used in solute transport applications, its validity has been questioned. Here, our goal is to investigate the effects of heterogeneity and mass transfer limitations on block-scale longitudinal dispersion and to evaluate under which conditions the Scheidegger parameterization is valid. We compute the relaxation time or memory of the system; changes in time with periods larger than the relaxation time are gradually leading to a condition of local equilibrium under which dispersion is Fickian. The method we use requires the solution of a steady-state advection-dispersion equation, and thus is computationally efficient, and applicable to any heterogeneous hydraulic conductivity K field without requiring statistical or structural assumptions. The method was validated by comparing with other approaches such as the moment analysis and the first order perturbation method. We investigate the impact of heterogeneity, both in degree and structure, on the longitudinal dispersion coefficient and then discuss the role of local dispersion and mass transfer limitations, i.e., the exchange of mass between the permeable matrix and the low permeability inclusions. We illustrate the physical meaning of the method and we show how the block longitudinal dispersivity approaches, under certain conditions, the Scheidegger limit at large Péclet numbers. Lastly, we discuss the potential and limitations of the method to accurately describe dispersion in solute transport applications in heterogeneous aquifers.

KW - Environmental Chemistry

KW - Water Science and Technology

KW - Heterogeneity and scale

KW - Longitudinal dispersion

KW - Numerical models

KW - Solute transport

KW - Aquifers

KW - Boltzmann equation

KW - Equations of state

KW - Groundwater

KW - Groundwater resources

KW - Hydrogeology

KW - Mass transfer

KW - Parameterization

KW - Perturbation techniques

KW - Porous materials

KW - Relaxation time

KW - Advection-dispersion equation

KW - Computationally efficient

KW - Hydrodynamic dispersions

KW - Longitudinal dispersion coefficient

KW - Longitudinal dispersions

KW - Longitudinal dispersivity

KW - Mass transfer limitation

KW - Dispersions

U2 - 10.1016/j.jconhyd.2017.09.004

DO - 10.1016/j.jconhyd.2017.09.004

M3 - Journal article

VL - 212

SP - 41

EP - 54

JO - Journal of Contaminant Hydrology

JF - Journal of Contaminant Hydrology

SN - 0169-7722

ER -